Question

Exercícios de equação do segundo grau:
a)6x²-x-5=0
b)3x²+7x-6=0

Answer 1

$a)6 x^{2} -x-5=0\\\\ a=6;b=-1;c=-5\\\\ \Delta=b^2-4ac\to \Delta=(-1)^2-4*6*(-5)\to \Delta=1+120\to \Delta=121\\\\ x= \frac{-b+- \sqrt{\Delta} }{2a} \to x= \frac{-(-1)+- \sqrt{121} }{2*6} \to x= \frac{1+- 11}{12} \to \\\\ x'= \frac{1+ 11}{12} \to x'= \frac{12}{12} \to x'=1\\\\ x''= \frac{1- 11}{12} \to x''= \frac{-10}{12} \to x''= -\frac{5}{6} \\\\ S=(1;-\frac{5}{6})$







$b)3 x^{2} +7x-6=0\\\\ a=3;b=7;c=-6\\\\ \Delta=b^2-4ac\to \Delta=7^2-4*3*(-6)\to \Delta=49+72\to \Delta=121 \\\\ x= \frac{-b+- \sqrt{\Delta} }{2a} \to x= \frac{-7+- \sqrt{121} }{2*3} \to x= \frac{-7+- 11}{6} \to\\\\ x'= \frac{-7+ 11}{6} \to x'= \frac{4}{6} \to x'= \frac{2}{3} \\\\ x''= \frac{-7- 11}{6} \to x''= \frac{-18}{6} \to x''=-3\\\\ S=(-3:\frac{2}{3})$